If x is an integer, then is x a prime number?

(1) x is a multiple of a prime number --> if x=2 then the asnwer is Yes, but if x=4 then the answer is NO. Not sufficient.

(2) x is a product of two integers --> the same here: if x=1*2=2 then the asnwer is Yes, but if x=1*4=4 then the answer is NO. Not sufficient.

(1)+(2) The same xample: if x=2 then the asnwer is Yes, but if x=4 then the answer is NO. Not sufficient.

Answer: E.
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let me just further elaborate on Bunuel
(1) let the prime number be 2 then 2*1= 2 this is a prime number
again 2*2 =4 this is not a prime number so both 2 and 4 are multiples of the prime number 2, but 2 is a prime number and 4 is not so (1) is not sufficient


similarly 6 is a product of 2 integers 3*2 and 6 is not a prime number
but 2 is also a multiple of 2 integers 1*2 and 2 is a prime number
so (2) is also not sufficient

Taking both (1) and (2)
First number 2 , (1) Is a multiple of a prime no.( 2*1)
(2) is the product of 2 integers (2*1)
and 2 is a prime number

second number 6, (1) Is a multiple of a prime no.( 3*2)
(2) is the product of 2 integers (3*2)

and 6 is not a prime number

as both 1 and 2 together do not give a consistent answer the answer is e

Hope I have understood it correctly ,

Thanks Bunuel

Dear Bunuel, Ireally confused here in statement 1 (x is a multiple of a prime number )

in the case 2*1= 2. where is x here ? does it is 1 or 2 ?

Does the statement 1 mean that 2k=x? where k any integre.

x is a multiple of a prime number --> x = prime*k = 2*1.
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Thank you Bunuel +1 KUDOS

Question is - is X a prime number? We can get two amswer - either Yes - x is PN or No-x is not PN. For me, both would be correct.

When we solve statement 1 and 2, each statement's answer shows that X is not a Prime # i.e. each statement provides an answer

However the answer is only emphasis on Yes answer. Since we do not get the Yes anwer from both statements, both are not sufficient. Why is that? Is this how we are supposed to think in DS problems

Hello

In DS questions of the form "Is... " we need to be able to answer with a clear-cut YES or a clear-cut NO. But there shouldnt be a confusion or a duality that both YES and NO are possible.

Statement 1 - x is a multiple of prime number. 2 is a prime number. Now both 2 and 6 are multiples of 2, but 2 is prime while 6 is not. So if x is a multiple of prime number, it could be either prime (in which case answer to the question asked is YES) or it could be not prime (in which case answer to the question asked is NO).
Since we are unable to establish a definite YES or a definite NO from this statement, this statement is NOT sufficient to answer the question.

Same goes with second statement.

But 1 on the real test is not a prime?

But 1 is not a prime number..

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Can We try x = 0 in this question. Please guide.